## Pages

### Geometric transformations in the coordinate plane with a hole punch

Last week, I wrote a post about using a hole punch to find function inverses in algebra. A few people asked on Facebook if the process would also work for geometric reflections, and it absolutely does!

In this post I share an easy, hands-on method for demonstrating reflections and rotations of geometric shapes and their coordinates in the coordinate plane. The video included in the post covers reflecting over the x-axis, over the y-axis and over the line y = x. This same method will work for reflecting over any line of symmetry in the coordinate plane, even linear equations. I then share an idea for showing geometric rotations with a hole punch.

1: Reflections

Above is a quick video showing how to use a hole punch and a template to reflect a geometric shape in the coordinate plane. I glued the colored paper behind the holes just so that they were easier to see on the video. This probably wouldn't be necessary in the classroom.

Here is the PDF of templates in my Google Drive. There are graphs to demonstrate inverse functions in there, too, so it's named hole punch inverse functions. But you'll find the geometric shapes in there, towards the end of the PDF.

2: Rotations

Geometric rotations in the coordinate plane. I added 3 templates into the PDF template file linked above to show geometric rotations with a hole punch.

The grid I used for this rotation is the blank template from the Google Drive file linked above.

I cut cut into half of the y-axis to show the clockwise rotation from quadrant 4 into quadrant 3. I've been posting the videos on my Facebook page and on my YouTube channel.

The hole punch that I used in the videos is a 1/8th-inch with a 2-inch reach. It looks like the one in this picture. I had gotten mine from a craft store years ago (probably in the paper craft aisle, though I can't remember exactly), but this screenshot came from Amazon.

*If you don't have this longer reaching hole punch, an alternative is to have students poke holes in the paper with their pencils. One teacher commented that she prints the templates smaller so that they can be glued into student notebooks. I thought that was a really great idea.

UPDATE: Teacher Eric Funke was super generous in creating and sharing a printable set of lessons he made based on the video and handouts in this post. You can make a copy of his lessons here in my Drive.

Geometric transformations activities